PHEN1120-Lab09

PHEN-1120 NPU / Fall 2023 Concave Mirror NAME: Sophie Perruffel, Michell Tejera, Olivia Whitmore, Conner Woods SECTION: 1 Lab09: Concave Mirror INTRODUCTION While we all feel familiar with the images, we see in plane mirrors, our experiences with their curved counterparts might be limited to cosmetic mirrors or the side view mirrors on automobiles. In this experiment, you will explore the characteristics of the real images formed by curved concave (or converging) mirrors. Then you will develop a mathematical relationship describing the relationship between the positions of the object and the real image formed by concave mirrors. OBJECTIVES In this experiment, you will • Use a concave mirror to produce real images. • Explore how the position of the object affects the appearance, orientation, and size of real images produced by a concave mirror. • Explore how mirror characteristics and the position of the object affect the appearance, orientation, and size of virtual images produced by a concave mirror. • Determine the relationship between object distance, image distance, focal length, and magnification in real images produced by a concave mirror. MATERIALS Mirror Set Dynamics System track Small plane mirror Optics Expansion Kit Data Set LENS-MIRROR EQUATION Write below the Lens-Mirror Equation. In the Lens-Mirror Equation, define by the letter p the distance between the light source and the lens and by the letter q the distance between the mirror and the image. p is also reported as “object distance” and q as the “image distance” . Define with the letter f the focal length of the mirror. The Lens-Mirror Equation is labelled as Equation 1 throughout the lab handout. 1

PHEN1120-Lab09 Concave Mirrors Equation 1 : 1 p + 1 q = 1 f MAGNIFICATION EQUATION Write below the Equation for the Magnification M of an optical system consisting of an object, a mirror of focal length f and a screen with an image. Define 𝒉 𝒐 the object size and 𝒉 𝒊 the image size. Use the letter p as the “object-distance” and the letter q as the “image distance”. This Magnification Equation is labelled as Equation 2 throughout this lab handout. Equation 2 : M = h’ h = − q p FOCAL LENGTH OF A CONVERGING (BICONVEX) LENS For the 8 “Object-Distance” p reported in Table1 , record in Table 1 the measured values q for the “Image-Distance” and in Table 2 the corresponding Image sizes. Complete Table 1 by calculating the Inverse of the “Object-Distance” (1/p) and report the corresponding value in the second column of Table 1 . Calculate also the Inverse of the “ImageDistance” (1/q) and report the corresponding value in the fourth column of Table 1 In the fifth column of Table 2 report the Magnification M corresponding to the ratio of the Image size to the Object size and the negative sign comes from the fact that the Image is inverted compared to the Object (the image has the arrow pointing down and the object has the arrow pointing up). Please complete the last two rows of Table 2 by calculating first the Magnification using Equation 2 and by performing an error analysis between the two Magnification. Take the Magnification reported in column 5 as “measured” and the magnification of column 6 as “expected”. As a reminder the error analysis equation is: (𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑 − 𝑒𝑥𝑝𝑒𝑐𝑡𝑒𝑑) 𝑃𝑒𝑟𝑐𝑒𝑛𝑡𝑎𝑔𝑒 𝐷𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 [%] = × 100 𝑒𝑥𝑝𝑒𝑐𝑡𝑒𝑑 2

PHEN1120-Lab09 Concave Mirrors Table 2 : Measured “Object-Distance” p and “Image-Distance” q, Image size 𝒉 𝒊 and Object size 𝒉 𝟎 . Object- Distance p [cm] Image- Distance q [cm] Image Size 𝒉 𝒊 [𝒄𝒎] Object Size 𝒉 𝒐 [𝒄𝒎] 𝒉 𝑴 = 𝒊 𝒉 𝟎 𝒒 𝑴 = − 𝒑 Difference [%] 25 19 3.5 4 0.875 0.76 -15.13% 30 16.5 2.5 4 0.625 0.55 13.363% 35 15 2 4 0.5 0.43 16.66% 40 14.3 1.5 4 0.375 0.3575 4.895% 45 14 1.5 4 0.375 0.3111 20.53% 50 13.3 1.1 4 0.275 0.266 3.38% 55 13 1.1 4 0.275 0.236 16.34% 60 12 1 4 0.25 0.2 25% ANALYSIS Q1 . Using the data reported in Table 1 , perform a plot with 1/p on the X-axis (second column of Table 1 ) and 1/q on the Y-axis (fourth column of Table 1 ). Label properly the X-axis, the Y-axis and please put a Title on your plot. Display the data of Table 1 as points (do not join the points with a line) and perform a Linear Fit of the data . Display clearly the coefficient of the linear fit on the plot. Please insert the plot below. 4

PHEN1120-Lab09 Concave Mirrors Q2. Following Equation 1, write an Equation below showing the relationship between the Yintercept of the Linear Fit reported in the plot of Q6 and the focal length of the mirror. This Equation is labelled Equation 3 in this lab handout. Equation 3 : 1/f=1/q+1/p Q3. Using Equation 3 and the Y-Intercept of the linear fit reported in the plot of Q6 determine the measured value of the focal length the mirror. Write the value of the measured focal length of the mirror below. 12.1 Q4. The focal length of the mirror used for the experiment reported in Table 1 is f=+10 cm from its design. Please take this f=+10 cm as the expected value of the focal length of the lens and take the value of the focal length reported in Q3 as the measured value of the focal length of the mirror. Perform an error analysis between the expected and measured values of the focal length of the mirror and report below the percentage difference. As a reminder, the error analysis equation is reported in the next page. 5